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A296171
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O.g.f. A(x) satisfies: [x^n] exp( n^2 * A(x) ) = [x^(n-1)] exp( n^2 * A(x) ) for n>=1.
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18
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1, -1, -1, -9, -134, -2852, -79096, -2699480, -109201844, -5100872244, -269903909820, -15944040740604, -1039553309158964, -74123498185170292, -5736368141560365292, -478780244956262592748, -42865943103053965559668, -4097785410628237071311764, -416572537937169684523985420, -44873737158384968851319470220, -5106038963454360810619516396820, -611986780692307637617151164361140, -77066319756799442735378541663266476
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OFFSET
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1,4
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COMMENTS
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E.g.f. G(x) of A296170 satisfies: [x^(n-1)] G(x)^(n^2) = [x^n] G(x)^(n^2) for n>=1.
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LINKS
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Paul D. Hanna, Table of n, a(n) for n = 1..300
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EXAMPLE
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G.f. A(x) = x - x^2 - x^3 - 9*x^4 - 134*x^5 - 2852*x^6 - 79096*x^7 - 2699480*x^8 - 109201844*x^9 - 5100872244*x^10 - 269903909820*x^11 - 15944040740604*x^12 - 1039553309158964*x^13 - 74123498185170292*x^14 - 5736368141560365292*x^15 + ...
such that
G(x) = exp(A(x)) = 1 + x - x^2/2! - 11*x^3/3! - 239*x^4/4! - 17059*x^5/5! - 2145689*x^6/6! - 412595231*x^7/7! - 111962826751*x^8/8! - 40590007936199*x^9/9! - 18900753214178609*x^10/10! + ... + A296170(n)*x^n/n! + ...
satisfies [x^(n-1)] G(x)^(n^2) = [x^n] G(x)^(n^2) for n>=1.
RELATED SERIES.
Series_Reversion(A(x)) = x + x^2 + 3*x^3 + 19*x^4 + 226*x^5 + 4259*x^6 + 110514*x^7 + 3626207*x^8 + 143043592*x^9 + 6567931068*x^10 + 343278693103*x^11 + 20092744961109*x^12 + 1300754163383700*x^13 + ... + A295812(n)*x^n + ...
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PROG
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(PARI) {a(n) = my(A=[1]); for(i=1, n+1, A=concat(A, 0); V=Vec(Ser(A)^((#A-1)^2)); A[#A] = (V[#A-1] - V[#A])/(#A-1)^2 ); polcoeff(log(Ser(A)), n)}
for(n=1, 30, print1(a(n), ", "))
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CROSSREFS
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Cf. A296170, A295812, A296173, A296175, A296177.
Sequence in context: A213688 A163200 A279975 * A167893 A268062 A218326
Adjacent sequences: A296168 A296169 A296170 * A296172 A296173 A296174
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KEYWORD
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sign
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AUTHOR
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Paul D. Hanna, Dec 07 2017
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STATUS
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approved
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